The generator matrix

 1  0  1  1  1  0  1  1  0  1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  0  X  X  X  1  1  1  1  0  0  1  0  1  0  1  1  0  X  X  0  0  0  1
 0  1  1  0  1  1  0 X+1  1  0  1 X+1  1  0  1  0 X+1  1  0 X+1  1  0  1  1  X X+1  1  X  1  1  X X+1  1  X  1  1  X X+1  1  X  1  1  X X+1  1  X  1  1  0  0  0  X  0  X  0  0  0  X  0  X  X  0  0  X  X  X  X  0  X  0  X  1  1 X+1  X X+1  X X+1  1  1  1  0  0  1  X X+1
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  X  0  X  X  0  X  0  X  0  0  X  0  0  X  0  0  X  0  0  0  0  0  X  X  X  X  0  X  0  X  0  X  X  0  X  X  0  0  X  X  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  X
 0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  0  0  X  X  X  0  X  X  0  0  X  X  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  X
 0  0  0  0  X  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  X  0  X  0  X  0  0  X  X  0  X  X  X  0  0  X  0  0  0  X  0  X  0  0  0  X  X  X  0  0
 0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0  0  X  0  X  0  X  0  X  0  X  0  X  X  0  X  0  X  0  X  0  0  X  0  X  X  0  X  0  0  X  0  0  X  X  0  X  X  X  X  X  X  X  0  X  X  X  0  0  X  X  X  X  X  X  X  0

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+22x^81+31x^82+26x^83+34x^84+18x^85+22x^86+26x^87+12x^88+18x^89+8x^90+6x^91+11x^92+6x^93+2x^94+6x^95+3x^96+1x^98+2x^100+1x^156

The gray image is a linear code over GF(2) with n=172, k=8 and d=81.
This code was found by Heurico 1.16 in 0.421 seconds.